Theorem 3.1 ([1]}, [2]})  
Let \(G\)  be a graph on \(n\)  vertices with \(\delta (G)\ge \delta \) . Then
\( \lambda (G) \le \frac{1}{2}\Bigl ( \delta -1 +\sqrt{8e(G) - 4\delta n + (\delta +1)^2} \Bigr ). \) 

